Mathematische Annalen

, Volume 288, Issue 1, pp 713–730 | Cite as

Extension functors of modular Lie algebras

  • Rolf Farnstein
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References

  1. 1.
    Abe, E.: Hopf algebras. Cambridge: Cambridge University Press 1980Google Scholar
  2. 2.
    Cartan, H., Eilenberg, S.: Homological algebra. Princeton, NJ: Princeton Univ. Press 1956Google Scholar
  3. 3.
    Chevalley, C., Eilenberg, S.: Cohomology theory of Lie groups and Lie algebras. Trans. Am. Math. Soc.63, 85–124 (1948)Google Scholar
  4. 4.
    Chiu, S., Shen, G.: Cohomology of graded Lie algebras of Cartantype of characteristicp. Abh. Math. Semin. Univ. Hamb.57, 139–156 (1986)Google Scholar
  5. 5.
    Dixmier, J.: Cohomologie des algèbres des Lie nilpotentes. Acta Sci. Math. (Szeged)16, 246–250 (1955)Google Scholar
  6. 6.
    Farnsteiner, R.: Central extensions and invariant forms of graded Lie algebras. Algebras Groups Geom.3, 431–455 (1986)Google Scholar
  7. 7.
    Farnsteiner, R.: Dual space derivations andH 2 (L, F) of modular Lie algebras. Can. J. Math.39, 1078–1106 (1987)Google Scholar
  8. 8.
    Farnsteiner, R.: On the cohomology of associative algebras and Lie algebras. Proc. Am. Math. Soc.99, 415–420 (1987)Google Scholar
  9. 9.
    Farnsteiner, R.: On the vanishing of homology and cohomology groups of associative algebras. Trans. Am. Math. Soc.306, 651–665 (1988)Google Scholar
  10. 10.
    Farnsteiner, R.: Cohomology groups of infinite dimensional algebras. Math. Z.199, 407–423 (1988)Google Scholar
  11. 11.
    Farnsteiner, R.: Beiträge zur Kohomologietheorie assoziativer Algebren. Habilitationschrift Hamburg 1989Google Scholar
  12. 12.
    Farnsteiner, R., Strade, H.: Shapiro's Lemma and its consequences in the cohomology theory of modular Lie algebras. Math. Z. (to appear)Google Scholar
  13. 13.
    Garland, H., Lepowsky, J.: Lie algebra homology and the Macdonald-Kac formulas. Invent. Math.34, 37–76 (1976)Google Scholar
  14. 14.
    Hilton, P.J., Stammbach, U.: A course in homological algebra. (Graduate Texts, Vol. 4) Berlin Heidelberg New York: Springer 1970Google Scholar
  15. 15.
    Hochschild, G.P.: On the cohomology groups of an associative algebra. Ann. Math.46, 58–67 (1945)Google Scholar
  16. 16.
    Jacobson, N.: A note on Lie algebras of characteristicp. Am. J. Math.74, 357–359 (1952)Google Scholar
  17. 17.
    Rotman, J.: An introduction to homological algebra. Vol. 85. Orlando: Academic Press 1979Google Scholar
  18. 18.
    Seligman, G.B.: Modular Lie algebras. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 40, Berlin Heidelberg New York: Springer 1967Google Scholar
  19. 19.
    Shen, G.: Graded modules of graded Lie algebras of Cartan type I. Scientica Sinica29, 570–581 (1986)Google Scholar
  20. 20.
    Shen, G.: Graded modules of graded Lie algebras of Cartan type II. Sci. Sin., Ser.A29, 1009–1019 (1986)Google Scholar
  21. 21.
    Shen, G.: Graded modules of graded Lie algebras of Cartan type III. Chin. Ann. Math., Ser.B9B, 404–417 (1988)Google Scholar
  22. 22.
    Strade, H.: Darstellungen auflösbarer Lie Algebren. Math. Ann.232, 15–32 (1978)Google Scholar
  23. 23.
    Strade, H.: The role ofp-envelopes in the theory of modular Lie algebras. Contemp. Math. (to appear)Google Scholar
  24. 24.
    Strade, H., Farnsteiner, R.: Modular Lie algebras and their representations. Textbooks and Monographs 116. New York: Dekker 1988Google Scholar
  25. 25.
    Whitehead, J.H.C.: On the decomposition of an infinitesimal group. Proc. Cambridge Philos. Soc.32, 229–237 (1936)Google Scholar
  26. 26.
    Whitehead, J.H.C.: Certain equations in the algebra of a semisimple infinitesimal group. Q. J. Math., Oxf. II. Ser.8, 220–237 (1937)Google Scholar
  27. 27.
    Williams, F.L.: The cohomology of semisimple Lie algebras with coefficients in a Verma module. Trans. Am. Math. Soc.240, 115–127 (1978)Google Scholar
  28. 28.
    Zassenhaus, H.: The representations of Lie algebras of prime characteristics. Proc. Glasgow Math. Ass.21, 1–36 (1954)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Rolf Farnstein
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMilwaukeeUSA

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